Michael J. Fox has said that he felt depressed and turned to alcohol when he was first diagnosed with the disease in 1991. "My first reaction to it was to start drinking heavily," he admitted last year. "I used to drink to party, but now I was drinking alone and … every day."

"Once I did that it was then about a year of like a knife fight in a closet, where I just didn't have my tools to deal with it," he said. Fox went to Alcoholics Anonymous and therapy to help him cope.

Fox Tweeted his reaction Thursday to the news of Williams's own struggle with the diagnosis, and noted that the Academy Award winner supported his foundation for Parkinson's research.

"Stunned to learn Robin had PD. Pretty sure his support for our Fdn predated his diagnosis. A true friend; I wish him peace."

Stunned to learn Robin had PD. Pretty sure his support for our Fdn predated his diagnosis. A true friend; I wish him peace.

"In Parkinson's, you get a lot of degeneration in brain circuitry, dopamine, seratonin and epinephrin," says Okun, who also authored Parkinson's Treatment: 10 Secrets to a Happier Life. "[When you] start to take away some of those chemicals that help keep the balance from depression, you could expect … that the depression would be worse in scenarios where it's contributing to a pre-existing problem."

"It's the largest unmet hurdle in the treatment of Parkinson's," explains Okun. "You feel hopeless and you don't feel like there's an answer, [but] if we're aggressive in these cases, we can often make patients feel better."

Treatment for depression caused by Parkinson's includes an "interdisciplinary approach" involving psychiatrists, neurologists and counseling psychologists, along with the antidepressants.

"It's important to keep in mind that there is a way to lead a more hopeful and happy life," says Okun. "People are living long lives with Parkinson's."

For more on Robin Williams's tragic death and his legacy as a comic genius, pick up the latest issue of PEOPLE, on newsstands Friday